DSE 2010 doubt...pls help

[Sris]

A Consumer has the utility function u(x,y)=xy. suppose the consumer demands bundle (x^*,y^*).now suppose the seller of good x offers a" buy one get one free " scheme. given this scheme the consumer buys the bundle ( xd,yd) and gets an additional xd for free.which of the following is true?

a) xd>x^* and yd>y^*
b) xd>x^* and yd=y^*
c) xd>x^* and yd<y^*
d) xd=x^* and yd=y^*

[onionknight]

This is an example of cobb douglas (x^a*y^b) preferences with the exponent in the utility function equal for both x and y (a=b=1). In case a consumer has such preferences, they spend a/a+b of their income on good x and b/a+b on good y (both equal to 1/2, in this case). When there's a buy one, get one scheme on good x, the price of good x is essentially reduced to half of its former price. But the consumer still spends half of their income on good x and half on good y. Since the price of x is halved, he'll end up with twice as much of x and the same amount of y. Xd=Xnew/2=x^*    Yd=Y^*

[Sris]

thank u onionknight...